Let me address your questions in this order: 1) "release"; 2) shoulder motion; and 3) missing putts to the right.
There is no such thing as a "release" of the putter thru impact that helps a sound shoulder stroke. The only possible meaning for a "release" in a shoulder stroke is one of these:
a) nothing changed and the shoulder frame stayed coordinated with the swinging of the putter head so no shape change occurred in the arms or hands or the relation of the shaft to the body;
b) the shoulders stopped or slowed while the arms and/or hands sped up in a whip-like acceleration thru impact; or
c) the shoulders pulled to the inside closing thru impact.
In golfer-speak, "release" has no clear definition, but is really referring to either b) or c) or both (and not a)), the speaker not knowing which he means and the listener not knowing which he might mean if the listener puzzles out any meaning at all from the term "release" in and of itself without explanation] as to its meaning for movement.
If you use an armsy / handsy stroke, there may be a "release" similar to what happens in the full swing, but my understanding is that you don't DO a release in the full swing, and it just happens naturally when you make a sound swing motion. So, by analogy, there ought not be anything for you to DO by way of "release" in the putting stroke even if you use an armsy / handsy stroke.
In a shoulder stroke, INSTEAD of a release in any sense, what is supposed to occur is that the stroke bottoms out effortlessly exactly at the natural bottom of the stroke arc and then rises very slightly thru impact with the ball after bottoming out. In this, the shoulder frame ought to naturally and effortlessly keep up with the putter head swinging -- not lead it and not lag behind it. This coordination will be true even if you POWER the thru-stroke: time the powering so that the putterhead stays coordinated with the shoulder frame, and more specifically with the lead shoulder.
A release unnecessarily complicates line and touch: did the "release" body action keep the putterface square and online or change it, and if it changed it did the squareness have the exactly required timing -- a requirement injected solely by using the release in the first place; and did you control the whip-like acceleration caused solely by the release so as not to mess up your touch and pace or distance control? Why buy these headaches in your putting?
Making the shoulder stroke is stupidly simple, but apparently requires explaining. If you put the shape of the setup in the arms and hands and shoulders back at the top of a backstroke and then relax the same muscle that did that movement, the stroke swings itself down and thru in the forward stroke and the golfer just lets the putterhead and arms and hands go wherever gravity takes them as he stands still and witnesses the stroke happen.
The "same" muscle that puts the "triangle" as a whole at the top of the backstroke is the left inner oblique abdominal muscle, which connects the left side of the rib cage with the left pelvis. The CONTRACTION of this muscles tugs the shoulder down towards the outside of the left knee. When used in a bent-over-the-ball putting address posture, this contraction sends the "triangle" back to the top of the backstroke. Once the body posture is at the top of the backstroke, the putter, hands and arms are being held against gravity's pull by this muscle remaining contracted. Allowing this same muscle to now relax "releases" the shoulder frame, arms, and hands, and putter to now fall down and swing beneath the steady neck and throat.
The muscles that "set" the shape of the "triangle" do not involve the inner oblique or the fluidity of the stroke motion in a shoulder stroke, and relaxing the inner oblique does not cause the shape of the "triangle" to dissolve into a loosey-goosey mess. Set the muscle tone of the triangle including grip pressure and muscle tone in the arms and shoulders, keep that tone steady during the motion, and then contract and relax the left inner oblique to perform thew backstroke and to ALLOW the downstroke. Then the free-fall swinging of the triangle and the putterhead will by itself MOVE the lead shoulder vertically up in the thru-stroke past impact.
This pattern of shoulder stroke (set form, make backstroke, ALLOW thru-stroke by its inherent form) teaches the body action form correctly. Then, if YOU power the thru-stroke instead of ALLOWING the thru-stroke to occur, that's fine, but you form better be the same form either way -- the lead shoulder rises vertically in the thru-stroke either way, or you get a pull.
To cement this motion in the shoulder stroke, focus on where you hands end up in a good shoulder stroke once they get past your lead foot. The hands in a good shoulder stroke stay a constant distance out from your thighs moving parallel along the putt line, and don't curl to the inside off this line too soon. So get your hands thru impact past the lead foot to this position and pay attention to it and then repeat this position when you make a stroke. Dave Stockton Jr. was taught by his dad to get this done by his dad standing in front of him down line near his left side holding the butt of a putter aimed horizontally at the back of his left hand at address about 1 foot down the line and then making sure Dave delivered the back of his left hand against the butt of the club in his thru-stroke.
MISSING PUTTS TO THE RIGHT
Aside from aiming the putterface to the right and then rolling the ball where aimed (which is not a stroke issue, but an aiming issue), missing putts to the right is caused by these STROKE MOTION problems:
1) allowing the putter face to open more than the shoulder stroke opens the face to the target line (if any) and then failing to deal with this excess, resulting in open-face impact that sends the ball off to the right / outside;
2) speeding the thru-stroke out of the grip pressure's ability to control the putter face so that the added speed plus the putter design "lags" the toe open and sends the ball off to the outside of the intended line; and/or
3) changing the alignment of the shoulders during the stroke to realign the shoulders to the outside thru impact in the forward stoke.
The first two flaws are cured by MINIMUM grip pressure and steady TIMING. Without minimum grip pressure, the physics of almost all putters (including heel-shafted, toe-hanging, and even face-balanced putters) will promote the toe gating open in the backstroke and then lagging more open in the forward stroke. To "handle" and prevent this, the golfer needs a MINIMUM grip pressure / muscle tone holding the putter. The FUNCTION of the grip is to make the putterface and putterhead orientation coordinate with the shoulder orientation. This means that during the stroke, the grip pressure has to be sufficient in anticipation of the swinging forces. When the grip coordinates the putterface with the shoulder alignment, the toe never swings open in relation to whatever the shoulders do. Therefore, as long as the shoulders are parallel to the target line when the forward stroke goes thru the impact zone, reqsquaring the shoulders thru impact will also make sure the putterface is square thru impact. For this, see the next discussion about the third flaw above.
The third motion flaw is cured by keeping the throat line matching the midline of the stroke, which is where the throat line starts in relation to the bottom lowest point of the stroke arc. the throat line should start square / perpendicular to the aim of the putterface at address, so the throat line matches the leading edge of the putterface from toe to heel. When the neck is perpendicular to the shoulder frame, this setting the throat line to the putter leading edge automatically sets the shoulder frame parallel to the target putt line and putterface aim at address. If the throat line is allowed to shift open or closed in relation to this address orientation during the stroke motion, this swinging of the throat will alter the alignment of the shoulder frame.
The flaw we are concerned with results in missing to the outside, and that is a swinging right of the throat (for a right-hander) during the backstroke to "close" the shoulders to the target line and then staying misaligned when the forward stroke tracks along the shoulder alignment (aiming now outside the target to the right). This happens sometimes when the lead shoulder starting the backstroke comes forward or when the rear shoulder tries to help the backstroke happen and draws back from the target line. Either way, the throat line follows the bad shoulder frame action in the making of the backstroke.
To avoid this, the thought in the making of the backstroke is a) don't shove the throat line off its square orientation above the bottom of the stroke, and b) don't mind a little tracking of the backstroke to the inside but just don't go nuts to the inside. Both of these considerations counsel: "take it easy in terms of timing and violence in the making of the backstroke." The lead shoulder shoves the setup's "triangle" shape down thru the fixed left arm (natural muscle tone above minimum but not overly stiff) to move the sole of the putterhead back and very slightly up towards the top of the backstroke. I teach this as a "striking of the match" by the shoulder move to start the stroke away from the bottom, imagining a kitchen friction match-head on the putter sole beneath the sweetspot that I "strike" with the shoulder shove back and away. It i biomechanically impossible for this sort of action to send the putterhead away from you across the target line resulting in a looping stroke, but it is not impossible for this action to be overdone and result in a realignment of the throat line and shoulder frame to the outside beyond the point the body will handle coming forward.
So long as you aim the shoulder "striking of the match" takeaway pretty much straight back and up, even if not perfectly so, and do this with non-violent mild timing, the throat line will remain squarely aligned and the body itself will naturally resquare the shoulders from the mild deviance of the backstroke, doing so by no later than the bottom of the stroke and before impact.
The body resquares the shoulders from mildly out of position to back to square at the bottom because the hips did not also get out of address posture during the backstroke. (whatever hip alignment you have is fine, so don't worry making the hips parallel to the target line -- worry about the shoulder frame alignment.) This results in a mild tension developing from the shoulder frame having "twisted" the abdomen muscles and tissues above the non-moving hips, and this elastic tension in the abdomen muscles / tissues guides the body back to relaxed-at-square when the shoulders realign with the original hip posture and this "twist" tension dissipates. Once the neutral feeling returns in the abdomen, you're square again with the shoulders parallel to the target line. The body can do this very naturally without attention so long as the hips are fairly stable during the backstroke, the throat line is not allowed to swing out of alignment by the over-vigor of the backstroke, and the shove-back is well-directed and not too violent or too quick for your body's ability to keep things stable.
As a test, stand near the baseboard of a wall, position the putterhead square to the wall with the putter's toe about 1/4th inch separated from touching the baseboard, square up the throat line to the wall so the shoulders align parallel to the wall, make the backstroke as described, and then make VERY VIGOROUS and VIOLENT forward stroke beneath a throat line that stays square to the wall, moving the shoulders vertically in the rocking. If your grip pressure can handle the violence, you can sling your shoulder frame down the line as hard and fast as you want without causing the stroke and putterhead to come out of square and straight down the line. The toe of the putterhead will "hew" along the wall no closer or farther off the wall than the initial 1/4th inch. You really cannot miss to the outside, even with this nutso stroke. This means that so long as the shoulders are parallel at the start of the forward stroke, even a VIOLENT shoulder action will not send the hands or putterhead out to the right, unless your shoulder motion is tilted off vertical and the lead shoulder migrates back from parallel to the target line in the thru-stroke. But if your shoulder action has a tilt, VIOLENCE will send the hands and the putterhead path out to the outside across the target line, even if your throat line stays square.
So, the formula / know-how is: set throat line to match putterface aim and hence square to the target line, set a minimum grip pressure, shove the lead shoulder back mildly above stable hip alignment to "strike the match" for a nice rhythmical backstroke impulse that starts the total swinging, and then either allow the down-and-thru stroke to complete itself coming forward with minimum unchanging grip pressure or move the forward stroke yourself non-violently with minimum unchanging grip pressure so the shoulders work vertically up from the surface and the back of the lead hand makes it past the front foot straight along the thighs without curling to the inside or getting cast to the outside or allowing the toe of the putter to flare open.
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